文章基本信息

标题：Formal Theories for Linear Algebra
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作者：Stephen Cook ; Lila Fontes
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2012
卷号：8
期号：1
页码：1
DOI：10.2168/LMCS-8(1:25)2012
出版社：Technical University of Braunschweig
摘要：We introduce two-sorted theories in the style of [CN10] for the complexity classes \oplusL and DET, whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys' linear algebra theory LAp over arbitrary integral domains, into each of our new theories. The result shows equivalences of standard theorems of linear algebra over Z2 and Z can be proved in the corresponding theory, but leaves open the interesting question of whether the theorems themselves can be proved.
其他关键词：logic, complexity classes, parity, determinant, linear algebra